What are the coordinates of the point on the directed line segment from ( − 10 , − 3 ) (−10,−3) to ( 2 , − 3 ) (2,−3) that partitions the segment into a ratio of 5 to 3?

Question

What are the coordinates of the point on the directed line segment from (−10,−3)(−10,−3) to (2,−3)(2,−3) that partitions the segment into a ratio of 5 to 3?

Answer 1

We want to split the segment from (-10,-3) to (2,-3) into segments of ratio of 5:3. Since the y coordinate is -3 for both coordinates, the y coordinate of the partitioning point will be -3. The ratio of 5:3 corresponds to 5/8 of the distance between x coordinates of the two points. So we would be moving 5/8 of the distance from -10 to 2 for the x coordinate, so the x coordinate would be -10 + 5/8 (12) = -2.5. So the coordinates of the point would be (-2.5,3)